1. The measure of angle GHI is 120°. Angle GHI is cut in half with ray HK, if angle
GHK is 3x + 48 , what is the value of x?

Step-by-step explanation:

Ray HK is an angle bisector, which means that it cuts the angle exactly in half.  So half of GHI is 60.  If GHK is 3x + 48, and that is half of angle GHI. then

3x + 48 = 60 and

3x = 12 so

x = 4

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.